This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and object-oriented programming and some other applications of LL, like semantics of negation in LP, non-monotonic issues in AI planning, etc. Although the overview covers pretty much the state-of-the-art in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...

The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1

In this paper we extend the notation of functional logic programs introduced in [1] by: (i) describing a formal translation of nested function references; (ii) dealing with set terms in the rule heads to allow non-determinism; and (iii) introducing high level constructions for representing action domains. The semantics we consider in this work, both for functional logic programs and for the actions language, just consists in a translation into (non-ground) logic programs under the answer sets semantics.

K is an executable semantic framework in which programming languages, calculi, as well as type systems or formal analysis tools can be defined making use of configurations, computations and rules. Configurations organize the system/program state in units called cells, which are labeled and can be nested. Computations carry “computational meaning ” as special nested list structures sequentializing computational tasks, such as fragments of program; in particular, computations extend the original language or calculus syntax. K (rewrite) rules generalize conventional rewrite rules by making it explicit which parts of the term they read-only, write-only, or do not care about. This distinction makes K a suitable framework for defining truly concurrent languages or calculi even in the presence of sharing. Since computations can be handled like any other terms in a rewriting environment, that is, they can be matched, moved from one place to another in the original term, modified, or even deleted, K is particularly suitable for defining control-intensive language features such as abrupt termination, exceptions or call/cc. This paper gives an overview of the K framework: what it is, how it can be used, and where it has been used so far. It also proposes and discusses the K definition of Challenge, a programming language that aims at challenging and exposing the limitations of the various existing semantic frameworks. 1.